`int_(0)^(pi//2)xcosxdx` `=?`

int_(0)^(pi)xcosxdx=-2

int_(0)^(pi//2)x^(2)cosxdx

int_0^(pi/2) e^-xcosxdx

int_0^(pi/2) e^-xcosxdx

int_(0)^((pi)/(4))xcosxdx

int_(0)^( pi/2)cosxsinxdx

int_(0)^(pi//2)sinxsin2xdx=?

int_(0)^(pi//2)sin^(2)xdx=?

Show that int_(0)^(pi//2) sin^(n)xdx =int_(0)^(pi//2) cos^(n)x dx .

Show that (i) int_(0)^(pi//2)f(sinx) d x=int_(0)^(pi//2)f(cos x) d x (ii) int_(0)^(pi//2)f(tan x) d x=int_(0)^(pi//2)f(cot x) d x (iii) int_(0)^(pi//2)f(sin 2 x) sin xd x = int_(o)^(pi//2)f(sin 2x).cosx d x